Image segmentation is a central topic in image processing and computer vision and a key 1 issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote 2 sensing. According to the human perception, image segmentation is the process of dividing an 3 image into non-overlapping regions. These regions, which may correspond to different objects, are 4 fundamental for the correct interpretation and classification of the scene represented by the image.
5The division into regions is not unique, but it depends on the application, i.e., it must be driven by 6 the final goal of the segmentation and hence by the most significant features with respect to that 7 goal. Image segmentation is an inherently ill-posed problem. A classical approach to deal with ill 8 posedness consists in the use of regularization, which allows us to incorporate in the model a-priori 9 information about the solution. In this work we provide a brief overview of regularized mathematical 10 models for image segmentation, considering edge-based and region-based variational models, as well 11 as statistical and machine-learning approaches. We also sketch numerical methods that are applied in 12 computing solutions coming from those techniques.